Multimode optical fiber and system comprising such fiber

ABSTRACT

One exemplary multimode optical fiber includes a graded index glass core having a diameter in the range of 41 microns to 80 microns, a graded index having an alpha less than 2.04 and a maximum relative refractive index in the range between 0.6% and 1.8%. The cladding includes a depressed-index annular portion. The fiber has an overfilled bandwidth greater than 2.5 GHz-km at at least one wavelength between 1200 nm and 1700 nm.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a Continuation-in-Part and claims the benefit ofpriority to U.S. Priority patent application Ser. No. 13/484,970, filedon May 31, 2012, the content of which is relied upon and incorporatedherein by reference in its entirety and the benefit of priority under 35U.S.C. Section 120 is hereby claimed.

BACKGROUND

The present invention generally relates to fiber optic communication,and more particularly relates to a multimode optical fiber that may beparticularly useful for use for wavelength division multiplexing in the1310 nm and/or the 1550 nm window.

High performance computing and data center installations typicallyrequire a large number of processor-to-processor interconnections, andusing multimode (MM) optical fibers in these systems is cost-effectivedue to more relaxed alignment tolerances due to the large core diameter.These systems typically operate in the 850 nm wavelength window,utilizing relatively inexpensive VCSEL laser sources. Optical fiber hasrelatively high dispersion at 850 nm, and this leads to rapid broadeningof the optical signals. This high dispersion is a key limitation for themaximum system length, particularly at data modulation rates of 25 GHzand higher. In addition, the fiber attenuation is relatively high at 850nm, and this negatively impacts the performance when the system lengthis more than a few tens of meters.

SUMMARY

According to some embodiments, a multimode optical fiber is provided.The fiber includes a graded index glass core having a diameter in therange 41 microns to 80 microns, a graded index having an alpha profilewherein 1.95≦α≦2.04 and a maximum relative refractive index in the rangebetween 0.6% and 1.8%, for example 0.6% to 1.6%. The fiber also includesa cladding surrounding in contact with the core. The cladding includes adepressed-index annular portion. The fiber further has an overfilledbandwidth greater than 2500 MHz-km at least one wavelength between 1200nm and 1700 nm (for example between 1260 nm and 1610 nm).

Preferably, core has a numerical aperture NA, where 0.16<NA<0.26.According to some embodiments the cladding includes an inner annularportion with relative refractive index delta Δ₂, measured at the radiallocation where the first derivative d(Δ/Δ_(1MAX))/d(r/R₁), is equal to−2.5.

According to some embodiments the cladding comprises an inner annularportion surrounding and in contact with the core, the depressed-indexannular portion surrounding the inner annular portion, and an outerannular portion surrounding and in contact with the depressed-indexannular portion.

High performance computing and data center installations typicallyrequire a large number of processor-to-processor interconnections, andusing multimode optical fibers discussed herein in these systems resultsin lower connector costs due to less stringent alignment tolerancescompared to systems that utilize single mode (SM) fibers. In addition,systems operating in the 1310 nm and/or 1550 nm windows offer asignificant performance advantage over conventional systems operating at850 nm due to lower fiber dispersion and attenuation. This isparticularly important at data modulation rates of 25 GHz and higher,where dispersive broadening of the optical signals results in largeimpairments. In addition, high data rate systems employingsilicon-photonic transceivers in the 1310 nm and/or 1550 nm windowsadvantageously require much less electrical power than conventionalVCSEL-based systems operating at 850 nm. The optical fibers and systemsdescribed herein can advantageously be used with both VCSEL andsilicon-photonic laser sources in the 1310 nm or 1550 nm windows.

There is a need for multimode optical fibers that are capable oftransmitting at least one signal modulated at 25 GHz or higher in the1310 nm window, over distances of at least 100 m. The fiber embodimentsdescribed herein are capable of transmitting at least four signalsmodulated at 25 GHz or higher in the 1310 nm window, over distances ofat least 100 m. Some fiber embodiments described herein are also capableof transmitting at least four signals modulated at 25 GHz or higher inthe 1310 nm window, over distances of at least 300 m. Some fiberembodiments described herein are also capable of transmitting at leastfour signals modulated at 25 GHz or higher in the 1310 nm window, overdistances of at least 500 m.

Similarly, there is a need for multimode optical fibers that are capableof transmitting at least one signal modulated at 25 GHz or higher in the1550 nm window, over distances of at least 100 m. The fiber embodimentsdescribed herein are capable of transmitting at least four signalsmodulated at 25 GHz or higher in the 1550 nm window, over distances ofat least 100 m. Some fiber embodiments described herein are also capableof transmitting at least four signals modulated at 25 GHz or higher inthe 1550 nm window, over distances of at least 300 m. Some fiberembodiments described herein are also capable of transmitting at leastfour signals modulated at 25 GHz or higher in the 1550 nm window, overdistances of at least 500 m.

Additional features and advantages will be set forth in the detaileddescription which follows, and in part will be readily apparent to thoseskilled in the art from that description or recognized by practicing theembodiments as described herein, including the detailed descriptionwhich follows, the claims, as well as the appended drawings.

It is to be understood that both the foregoing general description andthe following detailed description are merely exemplary, and areintended to provide an overview or framework to understanding the natureand character of the claims. The accompanying drawings are included toprovide a further understanding, and are incorporated in and constitutea part of this specification. The drawings illustrate one or moreembodiments, and together with the description serve to explainprinciples and operation of the various embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram (not to scale) of the refractive indexprofile of a cross section of the glass portion of an exemplaryembodiment of a multimode optical fiber having a depressed-index annularportion, according to one embodiment;

FIG. 2 is a cross-sectional view (not to scale) of the multimode opticalfiber of FIG. 1;

FIG. 3 is a graph illustrating the refractive index profile of anexemplary embodiment of the multimode optical fiber;

FIG. 3A is a graph illustrating the refractive index profile of anotherexemplary embodiment of the multimode optical fiber;

FIG. 4 is a graph illustrating the macrobend loss as a function ofwavelength of three exemplary embodiments of the multimode opticalfiber; and

FIG. 5 is a schematic illustration of a transmission system utilizingone embodiment of the multimode optical fiber.

DETAILED DESCRIPTION

Reference will now be made in detail to the present preferredembodiments, examples of which are illustrated in the accompanyingdrawings. Whenever possible, the same reference numerals will be usedthroughout the drawings to refer to the same or like parts.

The “refractive index profile” is the relationship between refractiveindex or relative refractive index and waveguide fiber radius.

The “relative refractive index” is defined as Δ=100×[n(r)²−n_(cl)²)]/2n(r)², where n(r) is the refractive index at the radial distance rfrom the fiber's centerline, and n_(cl) is the average refractive indexof the outer cladding at a wavelength of 1310 nm. Unless otherwisespecified, when the fiber diameter is 125 microns, n_(cl) is determinedby averaging the refractive index over a radius range between about 45and 55 microns, e.g.

$n_{cl} = {\sum\limits_{i = 1}^{N}{{n_{i}(r)}\text{/}N}}$

where there are N data points in the range 45≦r≦55 microns, and N atleast 2. In embodiments where the fiber diameter, 2*R₄, is not equal to125 microns, n_(cl) is determined by averaging the refractive index overa radius range between about 0.72*R₄ and 0.88*R₄. In one aspect, thecladding comprises essentially pure silica. In other aspects, thecladding may comprise silica with one or more dopants (e.g., GeO₂,Al₂O₃, P₂O₅, TiO₂, ZrO₂, Nb₂O₅ and/or Ta₂O₅) which increase the index ofrefraction, in which case the cladding is “up-doped” with respect topure silica. The cladding may also comprise silica with one or moredopants (e.g., F and/or B) which decrease the index of refraction, inwhich case the cladding “down-doped” with respect to pure silica. Asused herein, the relative refractive index is represented by delta or Δand its values are typically given in units of “%,” unless otherwisespecified. The terms: relative refractive index delta, delta, Δ, Δ%, %Δ,delta %, % delta and percent delta may be used interchangeabilityherein. In cases where the refractive index of a region is less thanthat of the cladding, the relative refractive index is negative and isreferred to as having a depressed index, and is calculated at the pointat which the relative index is most negative unless otherwise specified.In cases where the refractive index of a region is greater than therefractive index of silica, the relative refractive index is positiveand the region can be said to be raised or to have a positive index, andis calculated at the point at which the relative index is most positive,unless otherwise specified.

An “up-dopant” is herein considered to be a dopant which has apropensity to raise the refractive index relative to pure undoped SiO₂.A “down-dopant” is herein considered to be a dopant which has apropensity to reduce the refractive index relative to pure undoped SiO₂.An up-dopant may be present in a region of an optical fiber having anegative relative refractive index when accompanied by one or more otherdopants which are not up-dopants. Likewise, one or more other dopantswhich are not up-dopants may be present in a region of an optical fiberhaving a positive relative refractive index. A down-dopant may bepresent in a region of an optical fiber having a positive relativerefractive index when accompanied by one or more other dopants which arenot down-dopants. Likewise, one or more other dopants which are notdown-dopants may be present in a region of an optical fiber having anegative relative refractive index.

As used herein, the 1310 nm window is defined as the wavelength rangefrom 1200 nm to 1400 nm, or a subset of this wavelength range. Forexample, from 1260 to 1400 nm, 1260 to 1360 nm, 1270 to 1350 nm, 1280 to1340 nm or 1290 to 1330 nm (e.g., 1260 nm, 1290 nm, 1310 nm, 1330 nm,1350 nm, 1370 nm, or 1400 nm).

As used herein, the 1550 nm window is defined as the wavelength rangefrom 1500 nm to 1600 nm, or a subset of this wavelength range. Forexample, from 1520 to 1580 nm, 1530 to 1570 nm, 1540 to 1600 nm, 1540 to1580 nm or 1530 to 1570 nm (e.g., 1500 nm, 1510 nm, 1520 nm, 1530 nm,1540 nm, 1560 nm, 1570 nm, 1580 nm, 1590 nm or 1600 nm.)

As used herein, numerical aperture of the fiber means numerical apertureas measured using the method set forth in TIA SP3-2839-URV2 FOTP-177IEC-60793-1-43 titled “Measurement Methods and Text Procedures-NumericalAperture.”

The term graded index, “α-profile” or “alpha profile,” as used herein,refers to a relative refractive index profile, expressed in terms of Δwhich is in units of “%”, where r is the radius and which follows theequation,

${{\Delta (r)} = {\Delta_{0}\left\lbrack {1 - \left( \frac{r}{R_{1}} \right)^{\alpha}} \right\rbrack}},$

where Δ₀ is the relative refractive index extrapolated to r=0, R₁ is theradius of the core (i.e. the radius at which Δ(r) is zero (see FIG. 1)),and α is an exponent which is a real number. For a step index profile,the alpha value is greater than or equal to 10. For a graded indexprofile, the alpha value is less than 10. The term “parabolic,” as usedherein, includes substantially parabolically shaped refractive indexprofiles which may vary slightly from an α value of 2.0 at one or morepoints in the core, as well as profiles with minor variations and/or acenterline dip. The modeled refractive index profiles that exemplify theinvention have graded index cores which are perfect alpha profiles. Anactual fabricated fiber may have minor deviations from a perfect alphaprofile, including features such as dips or spikes at the centerlineand/or a diffusion tail at the outer interface of the core. Howeveraccurate values of alpha and Δ₀ may be obtained by numerically fittingthe measured relative refractive index profile to an alpha profile overthe radius range from 0.1 R₁≦r≦0.9 R₁. In ideal graded index fibers withno imperfections such as dips or spikes at the centerline, Δ₀=Δ_(1MAX),where Δ_(1MAX) is the maximum refractive index of the core. In othercases, the value from Δ₀ obtained from the numerical fit from 0.1R₁≦r≦0.9 R₁ may be greater or less than Δ_(1MAX).

Various embodiments of a multimode optical fiber exhibiting a corediameter which provides enhanced performance characteristics areprovided. Multimode optical fiber is disclosed having a graded indexglass core and a cladding surrounding and in contact with the core.According to the embodiments disclosed herein the core diameter is 41 toabout 80 microns. In some exemplary embodiments the core diameter isbetween about 60 and about 65 microns, which is comparable to the corediameter of commercially available 62.5 micron MMF. In other exemplaryembodiments the core diameter is between about 47 to about 53 microns,which is comparable to the core diameter of commercially available 50micron MMF. In some exemplary embodiments the core diameter is betweenabout 70 and 78 microns, which enables larger alignment tolerances forcoupling to optical transceivers. In other exemplary embodiments thecore diameter is between about 41 to about 50 microns, which reduces thenumber of propagating modes in the fiber and enables higher bandwidth.

The core also includes a graded index having an alpha (α) value of notless than 1.95 and not greater than 2.04, preferably equal to or lessthan 2.03, and more preferably between 1.96 and 2.03, and even morepreferably between 1.974 and 2.02 (for example, 1.974, 1.975, 1.976,1.978, 1.979, 1.98, 1.981, 1.982, 1.983, 1.985 1.99, 2.002, 2.006,2.007, 2.008, 2.009, 2.01, 2.012. 2.015 or there between). These alphavalues enable high fiber bandwidths in the 1310 nm window. The corefurther has a maximum refractive index in the range between 0.6% and1.8% (preferably 0.6% to 1.6%), for example, 0.6%, 0.65%, 0.7%, 0.8%,0.85%, 0.9%, 0.95%, 1%, 1.05%, 1.1%, 1.2%, 1.3%, 1.5%, 1.6%, 1.7%, 1.8%.In some embodiments the core has a maximum refractive index in the rangebetween 0.7% and 1.2%. In other embodiments the core has a maximumrefractive index in the range between 0.85% and 1.15%, preferablybetween 0.88% and 1.1%, and more preferably between 0.9% and 1.05%. Forexample, in some embodiments the core further has a maximum relativerefractive index delta of 0.9%, 0.93%; 0.95%; 0.98%; 1%; or 1.05%.

In the embodiments described herein the cladding includes adepressed-index annular portion. Preferably the cladding comprises aninner annular portion surrounding and in contact with the core, thedepressed-index annular portion surrounding the inner annular portion,and an outer annular portions surrounding and in contact with thedepressed-index annular portion.

In some embodiments the fiber as an overfilled bandwidth greater than2500 MHz-km at 1310 nm, and in some embodiments greater than 3750 MHz-kmat 1310 nm. In some embodiments the fiber further has an overfilledbandwidth greater than 5000 MHz-km at 1310 nm, and in some embodimentsthe fiber further has an overfilled bandwidth greater than 6000 MHz-kmor even 7500 MHz-km at 1310 nm. In some embodiments, the overfilledbandwidth is greater than 2500 MHz-km at all wavelengths in the rangefrom 1290 to 1330 nm, and in preferred embodiments, is greater than3750, 5000 or even 7500 MHz-km at all wavelengths in the range from 1290nm to 1330 nm. In other embodiments, the overfilled bandwidth is greaterthan 2500 MHz-km at all wavelengths in the range from 1270 to 1350 nm,and in preferred embodiments, is greater than 3750, 5000 or even 7500MHz-km at all wavelengths in the range from 1270 to 1350 nm. 1 GHz-km isequal to 1000 MHz-km.

In some embodiments the fiber as an overfilled bandwidth greater than2500 MHz-km at 1550 nm, and in some embodiments greater than 3750 MHz-kmat 1550 nm. In some embodiments the fiber further has an overfilledbandwidth greater than 5000 MHz-km at 1550 nm, and in some embodimentsthe fiber further has an overfilled bandwidth greater than 6000 MHz-kmor even 7500 MHz-km at 1550 nm. In some embodiments, the overfilledbandwidth is greater than 2500 MHz-km at all wavelengths in the rangefrom 1530 to 1570 nm, and in preferred embodiments, is greater than3750, 5000 or even 7500 MHz-km at all wavelengths in the range from 1530to 1570 nm. In other embodiments, the overfilled bandwidth is greaterthan 2500 MHz-km at all wavelengths in the range from 1510 to 1590 nm,and in preferred embodiments, is greater than 3750, 5000 or even 7500MHz-km at all wavelengths in the range from 1510 to 1590 nm. In someembodiments, the overfilled bandwidth is equal to or is greater than 5.0GHz-km at one or more wavelengths between 1500 nm and 1600 nm.

Referring to FIG. 1, a schematic representation of the refractive indexprofile of the cross section of the glass portion 10 of a multimodeoptical fiber 100 is shown, according one embodiment. The glass portion10 includes a graded index glass core 20 and a glass cladding 60 thatsurrounds the core 20 and is in contact with the core 20. The core 20may include silica doped with germanium, according to one embodiment.According to other embodiments, dopants other than germanium, such asAl₂O₃ or P₂O₅ singly or in combination, may be employed within the core20, and particularly at or near the centerline of the optical fiber 100.In this embodiment the cladding 60 includes an inner annular portion 30,a depressed-index annular portion 40, and an outer annular portion 50.The inner annular portion 30 surrounds and is in contact with the core20. The depressed-index annular portion 40 surrounds and is in contactwith the inner annular portion 30. The outer annular portion 50surrounds and is in contact with the depressed-index annular portion 40.The cladding 60 may further include additional portions (not shown) suchas further glass portions surrounding the outer annular portion 50. Thefiber 100 may further include a protective coating(s) including urethaneacrylate and acrylate primary and secondary coatings surrounding thecladding 60.

Referring to both FIGS. 1 and 2, the glass portion 10 of multimodeoptical fiber 100 is shown with the core 20 having an outer radius R₁.According some embodiments, the core outer radius R₁ is of 20.5>R₁>40microns, which corresponds to a core diameter between 41 microns and 80microns. For example, the core diameter may be 41, 42, 45, 48, 50, 55,60, 62.5, 65, 70, 72, 75, 78 or 80 microns, or therebetween. In someembodiments the graded index core has an alpha (α) value of not greaterthan 2.04. For example, in some embodiments (α) value is between 1.9 and2.04. In some embodiments the graded index core has an alpha (α) valueis between 1.98 and 2.02. In these embodiments, preferably, the glasscore 20 further has a maximum relative refractive index Δ_(1MAX) in therange of 0.6% to 1.6%, and in some embodiments is in the range of 0.7%to 1.2%.

In some embodiments the graded index core has an alpha (α) value isbetween 1.95 and 1.99 and preferably between 1.975 and 1.985. In theseembodiments, preferably, the glass core 20 further has a maximumrelative refractive index Δ_(1MAX) in the range of 0.7% to 1.6%, forexample between 1.75% and 1.55%

For example, in some embodiments α is 1.95, 1.97, 1.975, 1.976, 1.977,1.978, 1.98, 1.981, 1.982, 1.982, 1.983, 1.984, 1.985, 1.987, 1.99, 2.0,2.005, 2.007, 2.009, 2.01, 2.015, 2.02, 2.03 or 2.04, or therebetween.

According to one embodiment, the core outer radius R₁ is in the range of22.5 to 27.5 microns, which corresponds to a core diameter in the rangeof 45 microns to 55 microns. In some embodiments the graded index corehas an alpha (α) value of less than 2.04. For example, according to oneembodiment, the glass core 20 has a graded index having an alpha (α)value of about 1.97 to about 2.02. In this embodiment the glass core 20further has a maximum relative refractive index Δ_(1MAX) in the range of0.9% to 1.1%. According to another embodiment, the core graded index hasan alpha between 1.975 and 2.02 and the core 20 has a maximum relativerefractive index Δ_(1MAX) in the range of 0.95% to 1.05%.

According to one embodiment, the core outer radius R₁ is in the range of22.5 to 27.5 microns, which corresponds to a core diameter in the rangeof 45 microns to 55 microns. In some embodiments the graded index corehas an alpha (α) value of less than 2.04. For example, according to oneembodiment, the glass core 20 has a graded index having an alpha (α)value of about 1.97 to about 2.02. In this embodiment the glass core 20further has a maximum relative refractive index Δ_(1MAX) in the range of0.9% to 1.1%. According to another embodiment, the core graded index hasan alpha between 1.975 and 2.02 and the core 20 has a maximum relativerefractive index Δ_(1MAX) in the range of 0.95% to 1.05%.

The inner cladding portion 30 of cladding 60 has an outer radius R₂, awidth W₂, relative refractive index Δ₂, and a maximum relativerefractive index Δ_(2MAX). R₂ is defined as the radius at which thederivative of the normalized refractive index profile (also known as thenormalized slope and the normalized first derivative, herein) withrespect to the normalized radius, d(Δ/Δ_(1MAX))/d(r/R₁), is equal to−2.5, as shown in FIG. 3A. The refractive index Δ₂ is the relativerefractive index at the radius at which the first derivatived(Δ/Δ_(1max))/d(r/R₁) is equal to −2.5, Δ_(1max) being the maximum coredelta and R₁ being the core radius estimated by fitting the core indexprofile to an alpha profile, as described further below. The width W₂ ofthe inner cladding portion 30 may be in the range of 0.5 to 4.0 microns,and according to some embodiments preferably between 0.5 and 2.5microns, for example 0.5 μm≦W₂≦2.5 μm. The outer radius R₂ of the innercladding portion 30 is preferably in the range of 23 to 40 microns. Insome embodiments, the maximum relative refractive index Δ_(2MAX) of theinner cladding is less than about 0.1%. In other embodiments, themaximum relative refractive index Δ_(2MAX) of the inner cladding is lessthan about 0.0%. In other embodiments, the maximum relative refractiveindex Δ_(2MAX) of the inner cladding is between about −0.1% and about0.1%.

The depressed-index annular portion 40 of cladding 60 has a minimumrelative refractive index Δ_(3MIN) and extends from R₂ to R₃, wherein R₃is the radius at which Δ₃(r) first reaches a value of greater than−0.05%, going radially outwardly from the radius at whichΔ₃(r)=Δ_(3MIN). The depressed-index annular portion 40 has a radialwidth W₃=R₃−R₂. In one embodiment, the depressed-index annular portion40 has a width W₃ of at least 1 micron. W₃ is preferably between 2microns and 10 microns, more preferably between 2 microns and 8 micronsand even more preferably between 2 microns and 6 microns. Thedepressed-index annular portion 40 may have an outer radius R₃ in therange of 27 to 45 microns, more preferably 28 to 32 microns, for example30 to 45 microns, or 35 to 45 microns. The depressed-index annularportion 40 has a minimum relative refractive index Δ_(3MIN) less thanabout −0.2%, and more preferably refractive index Δ_(3MIN) may be in therange of −0.3% to −0.7%. The low index ring has a minimum relativerefractive Δ_(3MIN) which is less than or equal to Δ₂ and also less thanΔ_(1MAX).

The depressed-index annular portion has a profile volume, V₃, definedherein as:

V₃ = 2∫_(R₂)^(R₃)Δ₃(r)r r

where R₂ is the radius of the depressed-index annular portion as definedabove, and R₃ is the outer radius of the depressed-index annular portionas defined above. For the fibers disclosed herein, the absolutemagnitude of V₃ is preferably greater than 20%-μm², in some embodimentsgreater than 40%-μm², in other embodiments greater than 60%-μm², morepreferably greater than 80%-μm², for example: greater than 90%-μm²,greater than 95%-μm², greater than 100%-μm², or greater than 110%-μm².In some preferred embodiments, the absolute magnitude of V₃ is greaterthan 60%-μm² and less than 200%-μm². In other preferred embodiments, theabsolute magnitude of V₃ is greater than 80%-μm² and less than 160%-μm².In other preferred embodiments, the absolute magnitude of V₃ is greaterthan 80%-μm² and less than 140%-μm². In other preferred embodiments, theabsolute magnitude of V₃ is greater than 60%-μm² and less than 120%-μm².

In some embodiments, the depressed-index annular portion 40 comprisessilica doped with fluorine and/or boron. In some other embodiments, thedepressed-index annular portion 40 comprises voids, eithernon-periodically disposed, or periodically disposed, or both. By“non-periodically disposed” or “non-periodic distribution”, we mean thatwhen one takes a cross section (such as a cross section perpendicular tothe longitudinal axis) of the optical fiber, the non-periodicallydisposed voids are randomly or non-periodically distributed across aportion of the fiber. Similar cross sections taken at different pointsalong the length of the fiber will reveal different cross-sectional holepatterns, i.e., various cross sections will have different holepatterns, wherein the distributions of voids and sizes of voids do notmatch. That is, the voids or voids are non-periodic, i.e., they are notperiodically disposed within the fiber structure. These voids arestretched (elongated) along the length (i.e. parallel to thelongitudinal axis) of the optical fiber, but do not extend the entirelength of the entire fiber for typical lengths of transmission fiber.The voids can contain one or more gases, such as argon, nitrogen,krypton, CO₂, SO₂, or oxygen, or the voids can contain a vacuum withsubstantially no gas; regardless of the presence or absence of any gas,the refractive index in the annular portion 50 is lowered due to thepresence of the voids. While not wishing to be bound by theory, it isbelieved that the voids extend less than a few meters, and in many casesless than 1 meter along the length of the fiber. Optical fiber 100disclosed herein can be made by methods which utilize preformconsolidation conditions which are effective to result in a significantamount of gases being trapped in the consolidated glass blank, therebycausing the formation of voids in the consolidated glass optical fiberpreform. Rather than taking steps to remove these voids, the resultantpreform is used to form an optical fiber with voids, or voids, therein.As used herein, the diameter of a hole is the longest line segment whoseendpoints are disposed on the silica internal surface defining the holewhen the optical fiber is viewed in perpendicular cross-sectiontransverse to the longitudinal axis of the fiber.

According to some embodiments, the outer annular portion 50 of cladding60 has an outer radius R₄ and has relative refractive index Δ₄ which isgreater than Δ₂ and greater than Δ_(3MIN) and less than Δ_(1MAX).Accordingly, Δ_(1MAX)>Δ₄>Δ₂>Δ_(3MIN) in this embodiment. However, itshould be understood that other embodiments are possible. For example,Δ₄ may be equal to Δ₂ (see Table 1, for example). Alternatively, Δ₂ maybe greater than Δ₄. According to one embodiment, the outer radius R₄ isabout 62.5 microns, thereby resulting in an outer fiber diameter ofabout 125 microns.

The refractive index profile of a radially symmetric optical fiberdepends on the radial coordinate r and is independent of the azimuthalcoordinate φ. In most optical fibers, including the examples disclosedbelow, the refractive index profile exhibits only a small indexcontrast, and the fiber can be assumed to be only weakly guiding. Ifboth of these conditions are satisfied, Maxwell's equations can bereduced to the scalar wave equation, the solutions of which are linearlypolarized (LP) modes.

For a given wavelength, the radial equation of the scalar wave equationfor a given refractive index profile has solutions which tend to zerofor r going to infinity only for certain discrete values of thepropagation constant β. These eigenvectors (transverse electric field)of the scalar wave equation are guided modes of the fiber, and theeigenvalues are the propagation constants β_(lm), where l is theazimuthal index and m is the radial index. In a graded index fiber, theLP modes can be divided into groups, designated by common values of theprinciple mode number, p=l+2m−1. The modes in these groups have nearlydegenerate propagation constants and cutoff wavelengths and tend topropagate through the fiber with the same group velocity.

The numerical aperture (NA) is defined as the sine of the maximum angle(relative to the axis of the fiber) of the incident light that becomescompletely confined in the fiber by total internal reflection. It can beshown that this condition yields the relationship NA=√{square root over(n₁ ²−n_(cl) ²)}, where n₁ is the maximum refractive index of the gradedindex core. Using the definition of delta (Δ), this expression can betransformed into the following equation:

${NA} = {{n_{1}\sqrt{2\Delta}} = {n_{cl}\sqrt{\frac{2\Delta}{1 - {2\Delta}}}}}$

The overfilled bandwidth at a given wavelength is measured according tomeasurement standard FOTP-204 using an overfilled launch. The modeledbandwidth may be calculated according to the procedure outlined in T. A.Lenahan, “Calculation of Modes in an Optical Fiber Using the FiniteElement Method and EISPACK,” Bell Sys. Tech. J., vol. 62, pp. 2663-2695(1983), the entire disclosure of which is hereby incorporated herein byreference. Equation 47 of this reference is used to calculate the modaldelays; however note that the term dk_(cl)/dω² must be replaced with dk²_(cl)/dω², where k_(cl)=2π*n_(cl)/λ and ω=2π/λ. The modal delays aretypically normalized per unit length and given in units of ns/km. Thecalculated bandwidths also assume that the refractive index profile isideal, with no perturbations such as a centerline dip, and as a result,represent the maximum bandwidth for a given design.

Macrobend performance was determined according to FOTP-62(IEC-60793-1-47) by wrapping 2 turns around a either a 10 mm, 20 mm or30 mm diameter mandrel (e.g. “2×10 mm diameter macrobend loss” or the“2×20 mm diameter macrobend loss”) and measuring the increase inattenuation due to the bending using an encircled flux (EF) launchcondition. The encircled flux was obtained by launching an overfilledpulse into an input end of a 2m length of conventional (i.e. notbend-insensitive) 50 μm multimode optical fiber, which was deployed witha 1×25 mm diameter mandrel near the midpoint. The standard 50 micronmultimode fiber has a core diameter of about 50 microns, a numericalaperture of about 0.2 and a refractive index profile comprising a gradedindex core and a homogeneous cladding. The output end of the standard 50μm optical fiber was spliced to the fiber under test, and the measuredbend loss is the ratio of the attenuation under the prescribed bendcondition to the attenuation without the bend.

Multimode fiber 100 has an overfilled bandwidth greater than 2500 MHz-kmat at least one wavelength between 1290 nm and 1610 nm, and a numericalaperture NA less than 0.26, and preferably 0.16 to 0.26, more preferably0.17 to 0.21. Preferably, the overfilled bandwidth is greater than 3750MHz-km at either 1310 or 1550 nm, and in some embodiments greater than5000 MHz-km at 1310 nm at either 1310 or 1550 nm. Some fiber embodimentsdisclosed herein have the overfilled bandwidth is greater than 6000MHz-km at 1310 nm, and in some fiber embodiments have the overfilledbandwidth is greater than 7500 MHz-km at 1310 nm. In some embodiments,the overfilled bandwidth is greater than 2500 MHz-km at all wavelengthsin the range from 1290 to 1330 nm, and in preferred embodiments, isgreater than 3750 MHz-km, 5000 MHz-km or even 7500 MHz-km at allwavelengths in the range from 1290 to 1330 nm. In other embodiments, theoverfilled bandwidth is greater than 2500 MHz-km at all wavelengths inthe range from 1270 to 1350 nm, and in preferred embodiments, is greaterthan 3750, 5000 or even 7500 MHz-km at all wavelengths in the range from1270 nm to 1350 nm.

Some fiber embodiments disclosed herein have the overfilled bandwidth isgreater than 6000 MHz-km at 1350 nm, and in some fiber embodiments havethe overfilled bandwidth is greater than 7500 MHz-km at 1350 nm. In someembodiments, the overfilled bandwidth is greater than 2500 MHz-km at allwavelengths in the range from 1530 to 1570 nm, and in preferredembodiments, is greater than 3750 MHz-km, 5000 MHz-km or even 7500MHz-km at all wavelengths in the range from 1530 to 1570 nm. In otherembodiments, the overfilled bandwidth is greater than 2500 MHz-km at allwavelengths in the range from 1510 nm to 1590 nm, and in preferredembodiments, is greater than 3750, 5000 or even 7500 MHz-km at allwavelengths in the range from 1510 to 1590 nm.

Some fiber embodiments disclosed herein have a 2×10 mm macrobend lossless than 2 dB at 1310 nm, and other fiber embodiments have a 2×10 mmmacrobend loss less than 1.5 dB at 1310 nm. In some embodiments, the2×10 mm macrobend loss is less than 1.0 dB and in some examples is evenless than 0.8 dB at 1310 nm. Some fiber embodiments disclosed hereinhave a 2×15 mm macrobend loss less than 0.7 dB at 1310 nm, and otherfiber embodiments have a 2×15 mm macrobend loss less than 0.5 dB at 1310nm. In some embodiments, the 2×15 mm macrobend loss is less than 0.4 dBand in some examples is even less than 0.3 dB at 1310 nm. Some fiberembodiments disclosed herein have a 2×20 mm macrobend loss less than 0.6dB, and other fiber embodiments have a 2×20 mm macrobend loss less than0.4 dB at 1310 nm. In some embodiments, the 2×20 mm macrobend loss isless than 0.3 dB and in some examples is even less than 0.2 dB at 1310nm.

Some fiber embodiments disclosed herein have a 2×10 mm macrobend lossless than 2 dB at 1550 nm, and other fiber embodiments have a 2×10 mmmacrobend loss less than 1.5 dB at 1550 nm. In some embodiments, the2×10 mm macrobend loss is less than 1.0 dB and in some examples is evenless than 0.8 dB at 1550 nm. Some fiber embodiments disclosed hereinhave a 2×15 mm macrobend loss less than 0.7 dB at 1550 nm, and otherfiber embodiments have a 2×15 mm macrobend loss less than 0.5 dB at 1550nm. In some embodiments, the 2×15 mm macrobend loss is less than 0.4 dBand in some examples is even less than 0.3 dB at 1550 nm. Some fiberembodiments disclosed herein have a 2×20 mm macrobend loss less than 0.6dB, and other fiber embodiments have a 2×20 mm macrobend loss less than0.4 dB at 1550 nm. In some embodiments, the 2×20 mm macrobend loss isless than 0.3 dB and in some examples is even less than 0.2 dB at 1550nm.

EXAMPLES

Tables 1-4 summarizes various examples generally arranged in four setsof embodiments of multimode fibers that were modeled having variouscharacteristics in accordance with the invention disclosed herein andshown in FIG. 1. Various optical properties of the multi-mode fiberswere modeled from the refractive index profile parameters. Theseparameters include the relative refractive index Δ_(1MAX) of the core,outer core radius R₁, and the graded index alpha (α) parameter.Additionally, the parameters include the relative refractive index Δ₂ ofthe inner annular portion 40, the radius R₂ of the inner annular portion40, and the width W₂ of the inner annular portion 40. Further, theparameters include the minimum relative refractive index Δ_(3MIN) of thedepressed-index annular portion 50, and the outer radius R₃ of thedepressed-index annular portion 50. Further calculations include theoverfilled bandwidth at 1270 nm, 1280 nm, 1290 nm, 1310 nm, 1330 nm,1340 nm and 1350 nm, the number of propagating LP modes at 1310 nm, thedispersion and dispersion slope at 1310 nm, the attenuation at 1310 nm,the core diameter in microns, and the numerical aperture. In theexamples of Tables 1-4, the fiber has a high overfilled bandwidth (BW)in the 1310 nm window due (a) to the core having an (α) value between1.95 and 2.04, and (b) the optimized width W₂ of the inner annularportion 40. The optimum width for each embodiment depends on the maximumrelative refractive indices of the core, the inner annular portion andthe depressed index annular portion. These refractive index profilesenable an overfilled bandwidth greater than 2500 MHz-km at 1310 nm, andin some preferred embodiments, the overfilled bandwidth at 1310 nm isgreater than 3750, 5000 or even 7500 MHz-km. In some embodiments, theoverfilled bandwidth is greater than 2500 MHz-km at all wavelengths inthe range from 1290 to 1330 nm, and in preferred embodiments, is greaterthan 3750, 5000 or even 7500 MHz-km at all wavelengths in the range from1290 to 1330 nm. In other embodiments, the overfilled bandwidth isgreater than 2500 MHz-km at all wavelengths in the range from 1270 to1350 nm, and in preferred embodiments, is greater than 3750, 5000 oreven 7500 MHz-km at all wavelengths in the range from 1270 to 1350 nm.

Table 1 presents eight modeled embodiments in which the multimode fiber100 exhibits a core diameter between 45 and 55 microns and the core hasa maximum relative refractive index Δ_(1MAX) between 0.9% and 1%. Inthese exemplary fiber embodiments, 1.98≦α≦2.04, and in preferredembodiments is in the range 1.99≦α≦2.03. The overfilled bandwidth isgreater than 7500 MHz-km (7.5 GHz-km) at 1310 nm, and in someembodiments, is greater than 10 GHz-km or even 15 GHz-km at 1310 nm. Thenumerical apertures of these embodiments are between 0.185 and 0.215.The dispersion is less than 5 ps/nm/km at 1310 nm, and the attenuationis less than 0.7 dB/km at 1310 nm.

TABLE 1 Parameter Example 1 Example 2 Example 3 Example 4 Example 5Example 6 Example7 Δ_(1MAX) (%) 0.98 0.98 0.98 0.98 0.99 0.99 0.99 R1(microns) 24.80 23.54 23.67 23.72 25.00 24.6 24.6 α 2.007 2.007 2.0072.007 2.008 2.007 2.007 R2 (microns) 25.67 24.43 24.66 24.83 26.27 25.2425.76 Δ2 (%) 0 0 0 0 0 0 0 W2 (microns) 0.86 0.89 0.99 1.11 1.27 0.631.16 R3 (microns) 32 30 30 30 31 31.5 31.5 Δ_(3MIN) (%) −0.3 −0.34 −0.4−0.48 −0.55 −0.29 −0.29 W3 (microns) 6.34 5.58 5.34 5.17 4.74 6.27 5.74V3 (% microns²) 110 103 117 136 149 103 95 R4 (microns) 62.5 62.5 62.562.5 62.5 62.5 62.5 Δ4 (%) 0 0 0 0 0 0.03 −0.02 LP Modes 42 36 36 36 4236 42 BW1270 (GHz-km) 8.77 9.27 9.36 8.92 7.77 10.66 8.15 BW1280(GHz-km) 10.62 11.21 11.22 10.91 9.34 12.96 9.81 BW1290 (GHz-km) 13.0413.77 13.87 13.50 11.54 15.02 12.05 BW1310 (GHz-km) 16.40 17.78 17.8317.77 15.24 19.53 15.82 BW1320 (GHz-km) 17.26 12.83 12.28 12.10 9.7714.45 17.45 BW1330 (GHz-km) 14.18 10.14 9.56 9.30 7.31 11.54 14.72BW1340 (GHz-km) 11.51 8.15 7.61 7.31 11.41 9.37 12.04 Dispersion at 1310nm 0.42 0.42 0.42 0.42 0.37 0.48 0.48 (ps/nm/km) Dispersion Slope at0.10 0.10 0.10 0.10 0.10 0.10 0.10 1310 nm (ps/nm²/km) Attenuation at1310 0.33 0.33 0.33 0.33 0.33 0.33 0.33 nm (dB/km) Core Diameter 49.647.08 47.34 47.44 50 49.2 49.2 (microns) Numerical Aperture 0.206 0.2070.207 0.207 0.208 0.205 0.205

Table 2 presents seven embodiments in which the multimode fiber 100exhibits a core diameter between 41 and 80 microns and the core has amaximum relative refractive index Δ_(1MAX) between 0.8% and 1.3%. Inthese exemplary fiber embodiments, 1.98≦α≦2.04, and in preferredembodiments is in the range 1.99≦α≦2.03. The overfilled bandwidth isgreater than 7500 MHz-km (7.5 GHz-km) at 1310 nm, and in someembodiments, is greater than 10 GHz-km or even 15 GHz-km at 1310 nm. Thenumerical apertures of these embodiments are between 0.185 and 0.215.The magnitude of the dispersion is less than 5 ps/nm/km at 1310 nm, andthe attenuation is less than 0.7 dB/km at 1310 nm.

TABLE 2 Parameter Example 8 Example 9 Example 10 Example 11 Example 12Example 13 Example 14 Δ_(1MAX) (%) 0.90 0.99 0.98 1.00 1.10 1.10 1.20 R1(microns) 23.4 32 31.25 20.5 35.6 25 29 α 2.008 2.006 2.006 2.008 2.0052.006 2.005 R2 (microns) 24.47 33.13 32.36 21.32 36.97 25.82 30.11 Δ2(%) 0 0 0 0 0 0 0 W2 (microns) 1.07 1.13 1.11 0.82 1.37 0.82 1.11 R3(microns) 30.8 38 39 27 41 31 36 Δ_(3MIN) (%) −0.4 −0.32 −0.3 −0.35−0.42 −0.32 −0.44 W3 (μm) 6.33 4.87 6.64 5.68 4.03 5.18 5.90 V3 (%microns²) 140 111 142 96 132 94 171 R4 (microns) 62.5 62.5 62.5 62.562.5 62.5 62.5 Δ4 (%) 0 0 0 0 0 0 0 LP Modes 30 64 64 30 90 42 36 BW1270(GHz-km) 11.29 9.83 8.63 8.13 7.30 8.73 7.3732 BW1280 (GHz-km) 12.6711.30 10.33 9.83 8.51 10.42 8.3911 BW1290 (GHz-km) 12.12 13.81 12.5612.17 10.03 11.87 9.8637 BW1310 (GHz-km) 24.47 17.11 15.91 16.53 12.3215.40 11.5609 BW1320 (GHz-km) 16.84 12.10 16.40 19.60 9.24 12.16 8.6346BW1330 (GHz-km) 12.65 9.56 13.55 16.52 10.33 9.90 6.9373 BW1340 (GHz-km)9.81 7.68 11.00 13.30 8.68 8.11 5.5955 Dispersion at 1310 nm 0.77 0.370.43 0.46 −0.01 0.05 −0.33 (ps/nm/km) Dispersion Slope at 0.10 0.10 0.100.10 0.10 0.10 0.1 1310 nm (ps/nm2/km) Attenuation at 1310 0.33 0.330.33 0.33 0.33 0.33 0.326 nm (dB/km) Core Diameter 46.8 64 62.5 41 71.250 58 (microns) Numerical Aperture 0.196 0.206 0.205 0.207 0.217 0.2170.226

Table 3 presents six embodiments in which the multimode fiber 100exhibits a core diameter between 41 and 80 microns and the core has amaximum relative refractive index Δ_(1MAX) between 0.6% and 1.6%. Inthese exemplary fiber embodiments, 1.98≦α≦2.04, and in preferredembodiments is in the range 1.99≦α≦2.03. The overfilled bandwidth isgreater than 7500 MHz-km (7.5 GHz-km) at 1310 nm, and in someembodiments, is greater than 10 GHz-km or even 15 GHz-km at 1310 nm. Themagnitude of the dispersion is less than 5 ps/nm/km at 1310 nm, and theattenuation is less than 0.7 dB/km at 1310 nm. In a subset of theseembodiments, the core diameter is between 50 and 80 microns, and thecore has a maximum relative refractive index Δ_(1MAX) between 1.3% and1.6%. The numerical aperture of this subset of the embodiments isbetween 0.23 and 0.26. In another subset of these embodiments, the corediameter is between 41 and 50 microns, and the core has a maximumrelative refractive index Δ_(1MAX) between 0.6% and 0.9%. The numericalaperture of this subset of the embodiments is between 0.16 and 0.19.

TABLE 3 Parameter Example 15 Example 16 Example 17 Example 18 Example 19Example 20 Δ_(1MAX) (%) 1.35 1.36 1.55 1.50 0.65 0.65 R1 (microns) 31.2525.00 31.25 37.50 21.10 24.50 α 2.005 2.007 2.005 2.005 2.009 2.007 R2(microns) 32.035 25.69 31.94 38.94 22.04 25.71 Δ2 (%) 0 0 0 0 0 0 W2(microns) 0.78 0.69 0.69 1.44 0.94 1.21 R3 (microns) 39.00 32.00 39.0043.50 29.00 31.00 Δ_(3MIN) (%) −0.28 −0.32 −0.28 −0.65 −0.25 −0.32 W3(microns) 6.97 6.31 7.06 4.56 6.96 5.29 V3 (% microns²) 139 116 140 24489 96 R4 (microns) 62.5 62.5 62.5 62.5 62.5 62.5 Δ4 (%) 0 0 0 0 0 0 LPModes 81 56 100 132 20 25 BW1270 (GHz-km) 6.84 7.79 6.41 5.19 11.36 8.72BW1280 (GHz-km) 7.54 8.52 6.32 5.37 13.57 12.24 BW1290 (GHz-km) 7.958.76 5.93 5.90 16.84 14.70 BW1310 (GHz-km) 8.55 7.55 4.79 5.08 29.9021.82 BW1320 (GHz-km) 6.61 5.74 4.34 4.06 34.67 21.52 BW1330 (GHz-km)5.73 5.00 3.84 3.57 25.08 17.18 BW1340 (GHz-km) 5.00 5.20 3.43 3.5918.24 13.41 Dispersion at 1310 nm −0.91 −0.88 −1.67 −1.52 1.64 1.61(ps/nm/km) Dispersion Slope at 0.10 0.10 0.10 0.10 0.10 0.10 1310 nm(ps/nm²/km) Attenuation at 1310 0.33 0.33 0.33 0.33 0.33 0.33 nm (dB/km)Core Diameter 62.5 50 62.5 75 42.2 49 (microns) Numerical Aperture 0.2410.241 0.259 0.254 0.166 0.166

Table 4 presents eight embodiments in which the multimode fiber 100exhibits a core diameter between 41 and 80 microns and the core has amaximum relative refractive index Δ_(1MAX) between 0.6% and 0.9%. Inthese exemplary fiber embodiments, 1.98≦α≦2.04, and in preferredembodiments is in the range 1.99≦α≦2.03. The overfilled bandwidth isgreater than 7500 MHz-km (7.5 GHz-km) at 1310 nm, and in someembodiments, is greater than 10 GHz-km or even 15 GHz-km at 1310 nm. Themagnitude of the dispersion is less than 5 ps/nm/km at 1310 nm, and theattenuation is less than 0.7 dB/km at 1310 nm. The numerical aperturesof these embodiments are between 0.16 and 0.19. In some embodiments, thecore diameter is between 45 and 55 microns, in other embodiments thecore diameter is in between 60 and 65 microns, and in other embodiments,the core diameter is in between 41 and 50 microns.

TABLE 4 Refractive index profile parameters and modeled bandwidths.Parameter Example 21 Example 22 Example 23 Example 24 Example 25 Example26 Example 27 Example 28 Δ_(1MAX) (%) 0.75 0.75 0.75 0.752 0.756 0.7550.749 0.79 R1 (microns) 31.25 25 25 25 25 25 20.52 24.7 α 2.009 2.0092.010 2.010 2.011 2.010 2.010 2.010 R2 (microns) 32.83 26.15 26.36 26.4626.56 26.62 21.47 25.41 Δ2 (%) 0 0 0 0 0 0 0 0 W2 (microns) 1.58 1.151.36 1.46 1.56 1.62 0.95 0.71 R3 (μm) 38 31.5 30.5 31 31 31 28 31.5Δ_(3MIN) (%) −0.4 −0.32 −0.44 −0.5 −0.6 −0.67 −0.32 −0.32 W3 (microns)5.17 5.36 4.14 4.54 4.45 4.38 6.53 6.09 V3 (%-sq. microns) 146 99 104130 153 169 103 111 R4 (microns) 62.5 62.5 62.5 62.5 62.5 62.5 62.5 62.5Δ4 (%) 0 0 0 0 0 0 0 0.04 LP Modes 49 30 30 30 30 30 20 30 BW1270(GHz-km) 9.92 11.24 11.91 10.97 11.23 10.40 13.88 12.29 BW1280 (GHz-km)11.91 13.71 14.80 13.76 15.15 13.27 17.96 15.29 BW1290 (GHz-km) 14.8417.44 19.31 17.71 19.95 17.09 24.08 19.88 BW1310 (GHz-km) 21.89 29.1329.79 29.76 29.88 29.01 36.97 30.11 BW1320 (GHz-km) 14.35 20.92 16.9618.32 15.62 17.16 20.14 18.24 BW1330 (GHz-km) 10.44 15.19 12.32 12.9911.25 12.03 14.87 13.52 BW1340 (GHz-km) 19.43 11.50 9.41 9.71 8.54 8.9211.56 18.29 Dispersion at 1310 1.22 1.27 1.27 1.26 1.25 1.25 1.32 1.27nm (ps/nm/km) Dispersion Slope at 0.10 0.10 0.10 0.10 0.10 0.10 0.100.10 1310 nm (ps/nm²/km) Attenuation at 1310 0.32 0.33 0.33 0.33 0.330.33 0.33 0.33 nm (dB/km) Core Diameter 62.5 50 50 50 50 50 41.04 49.4(microns) Numerical Aperture 0.179 0.179 0.179 0.179 0.179 0.179 0.1780.179

As can be seen from Tables 1-4, each of the fiber Examples 1-28 haveoverfilled bandwidths at 1310 nm greater than 2500 MHz-km. According tosome at least some embodiments, the fibers have an overfilled bandwidthgreater than 5000 MHz-km at 1310 nm. According to at least someembodiments the fibers have an overfilled bandwidth greater than 7.5GHz-km at 1310 nm. According to at least some embodiments the fibershave an overfilled bandwidth greater than 10 GHz-km at 1310 nm.According to at least some embodiments the fibers have an overfilledbandwidth greater than 20 GHz-km at 1310 nm. In some embodiments, theoverfilled bandwidth is greater than 2500 MHz-km at all wavelengths inthe range from 1290 nm to 1330 nm, and in preferred embodiments, isgreater than 3750, 5000 or even 7500 MHz-km at all wavelengths in therange from 1290 nm to 1330 nm. In other embodiments, the overfilledbandwidth is greater than 2500 MHz-km at all wavelengths in the rangefrom 1270 nm to 1350 nm, and in preferred embodiments, is greater than3750, 5000 or even 7500 MHz-km at all wavelengths in the range from 1270nm to 1350 nm.

The fiber examples in Table 1 illustrate that a multi-mode fiber with agraded index core diameter in the range of 45 microns to 55 microns anda cladding surrounding the core and comprising a depressed-index annularportion. These fiber examples have an overfilled bandwidth greater than2.5 GHz-km at 1310 nm. More specifically, the fibers of Table 1 haveoverfilled bandwidths greater than 5 GHz-km at 1310 nm, and even greaterthan 10 GHz-km at 1310 nm. Similarly, Table 2 illustrates fibers withoverfilled bandwidths greater than 11.5 GHz-km at 1310 nm, and evengreater than 15 GHz-km at 1310 nm.

Preferably, the fibers have numerical apertures that are less than 0.21and the core comprises an alpha value less than 2.02 (and preferably<2.01). At least some of these fiber embodiments (see, for example,exemplary fibers 8, and 19-28) have very large overfilled bandwidths,for example greater than 20 GHz-km at 1310 nm.

Manufactured Fiber Examples 29-32 Example 29

A one meter long×26.15 mm diameter solid glass cane comprising aGeO₂—SiO₂ graded index core (approximately 0.75% maximum refractiveindex relative to pure silica with an approximately parabolic shape) wasloaded onto a lathe. 85 grams of SiO₂ (0.36 g/cc density) soot wereflame deposited onto the cane, and the assembly was dried for 2 hours inan atmosphere consisting of helium and 3% chlorine at 1000° C. This stepwas followed by down driving at 6 mm/min through a hot zone set at 1500°C. in a 100% helium atmosphere, in order to sinter the soot to anoptical preform comprising a GeO₂—SiO₂ graded index core and a silicafirst cladding layer. The preform was then loaded onto a lathe and 547grams of SiO₂ (0.36 g/cc density) soot were flame deposited and sinteredas follows. The assembly was first dried for 1 hour in an atmosphereconsisting of helium and 3% chlorine at 1125° C., followed by a purge inhelium environment at 1125° C. for 30 minutes. The assembly was thendown driven at 14 mm/min through a hot zone set at 1460° C. in anatmosphere comprising helium and 7.4% SiF₄ in order to sinter the sootto an overclad preform comprising a germania-silica graded index core, asilica inner cladding, and a fluorine-doped second cladding layer. Thepreform was drawn into a one meter×18.75 mm diameter cane, which wasthen placed on a lathe where 1879 grams of SiO₂ soot were flamedeposited. The assembly was then sintered by first drying it for 2 hoursin an atmosphere consisting of helium and 3% chlorine at 1000° C.,followed by down driving at 6 mm/min through a hot zone set at 1500° C.in a 100% helium atmosphere. This process sintered the soot into anoptical preform comprising a GeO₂—SiO₂ graded index core, a silica firstcladding layer, a fluorine-doped second cladding layer and a silicaouter cladding. The preform was then placed for 24 hours in an argonpurged holding oven set at 1000° C. The preform was drawn to a 10 kmlength of 125 micron diameter fiber at 10 m/s using a draw furnacehaving a hot zone of about 8 cm length and set at approximately 2000° C.The measured characteristics of the fiber are set forth in Table 5.

Example 30

A one meter long×26.04 mm diameter preform comprising a GeO₂—SiO₂ gradedindex core (approximately 0.91% maximum refractive index relative topure silica with an approximately parabolic shape) and a silica firstcladding was loaded onto a lathe. The ratio of the diameter of thegraded index core to the diameter of the glass preform was approximately0.94. 596 grams of SiO₂ (0.36 g/cc density) soot were flame depositedand sintered as follows. The assembly was first dried for 1 hour in anatmosphere comprising helium and 3% chlorine at 1125° C., followed by apurge in helium environment at 1125° C. for 30 minutes. The assembly wasthen down driven at 14 mm/min through a hot zone set at 1460° C. in anatmosphere consisting of helium and 4.76% SiF₄ in order to sinter thesoot to an overclad preform comprising a germania-silica graded indexcore, a silica inner cladding, and a fluorine-doped second claddinglayer. The preform was then placed on a lathe where 3575 grams of SiO₂soot were flame deposited. The assembly was then sintered by firstdrying it for 2 hours in an atmosphere consisting of helium and 3%chlorine at 1000° C., followed by down driving at 6 mm/min through a hotzone set at 1500° C. in a 100% helium atmosphere. This process sinteredthe soot into an optical preform comprising a GeO₂—SiO₂ graded indexcore, a silica first cladding layer, a fluorine-doped second claddinglayer and a silica outer cladding. The preform was then placed for 24hours in an argon purged holding oven set at 1000° C. The preform wasdrawn to a 10 km length of 125 micron diameter fiber at 10 m/s using adraw furnace having a hot zone of about 8 cm length and set atapproximately 2000° C. The measured characteristics of the fiber are setforth in Table 5.

Example 31

A one meter long×17.93 mm diameter preform comprising a GeO₂—SiO₂ gradedindex core (approximately 0.91% maximum refractive index relative topure silica with an approximately parabolic shape) and a silica firstcladding was loaded onto a lathe designed for outside vapor deposition.The ratio of the diameter of the graded index core to the diameter ofthe glass perform was approximately 0.94. 172 grams of SiO₂ (0.36 g/ccdensity) soot were flame deposited and sintered as follows. The assemblywas first dried for 1 hour in an atmosphere consisting of helium and 3%chlorine at 1125° C., followed by a purge in helium environment at 1125°C. for 30 minutes. The assembly was then down driven at 14 mm/minthrough a hot zone set at 1460° C. in an atmosphere consisting of heliumand 7.4% SiF₄ in order to sinter the soot to an overclad preformcomprising a germania-silica graded index core, a silica inner cladding,and a fluorine-doped second cladding layer. The preform was then placedon a lathe where 1255 grams of SiO₂ soot were flame deposited. Theassembly was then sintered by first drying it for 2 hours in anatmosphere consisting of helium and 3% chlorine at 1000° C., followed bydown driving at 6 mm/min through a hot zone set at 1500° C. in a 100%helium atmosphere. This process sintered the soot into an opticalpreform comprising a GeO₂—SiO₂ graded index core, a silica firstcladding layer, a fluorine-doped second cladding layer and a silicaouter cladding. The preform was then placed for 24 hours in an argonpurged holding oven set at 1000° C. The preform was drawn to a 10 kmlength of 125 micron diameter fiber at 10 m/s using a draw furnacehaving a hot zone of about 8 cm length and set at approximately 2000° C.The measured characteristics of the fiber are set forth in Table 5.

Example 32

A one meter long×18.08 mm diameter preform comprising a GeO₂—SiO₂ gradedindex core (approximately 0.93% maximum refractive index relative topure silica with an approximately parabolic shape) was loaded onto alathe designed for outside vapor deposition. 1255 grams of SiO₂ sootwere flame deposited and sintered as follows. The assembly was firstdried for 2 hours in an atmosphere consisting of helium and 3% chlorineat 1000° C., followed by down driving at 6 mm/min through a hot zone setat 1500° C. in a 100% helium atmosphere. This process sintered the sootinto an optical preform comprising a GeO₂—SiO₂ graded index core, and asilica outer cladding. The preform was then placed for 24 hours in anargon purged holding oven set at 1000° C. The preform was drawn to a 10km length of 125 micron diameter fiber at 10 m/s using a draw furnacehaving a hot zone of about 8 cm length and set at approximately 2000° C.The measured characteristics of the fiber are set forth in Table 5.

Table 5 presents Examples 29-32 in which the multimode fiber 100exhibits a core diameter between 45 and 65 microns, and the core has amaximum relative refractive index Δ_(1MAX) between 0.7% and 1.2%. Inexamples 29-31, the inner annular portion 30 comprises a width W₂greater than about 0.5 and less than about 4 microns. In exemplary fiberembodiments 29, 30 and 31, 1.98≦α≦2.04. Example 32 has an alpha valuegreater than 2.06 and does not comprise an inner annular portion with adepressed index, and as a result, the overfilled bandwidth is less than2500 MHz-km at 1300 nm. The overfilled bandwidth of examples 29-31 isgreater than 3750 MHz-km (3.75 GHz-km) at 1300 nm, and in examples 30and 31, is greater than 7.5 GHz-km at 1300 nm. The overfilled bandwidthof example 31 is also greater than 10 GHz-km at 1300 nm. The numericalaperture of these embodiments is between 0.16 and 0.24, and are between0.185 and 0.215 for examples 30 and 31. The attenuation at 1310 nm isless than 0.7 dB km for Examples 29-31 and less than 0.5 dB/km forExamples 30 and 31.

TABLE 5 Exam- Exam- Exam- Exam- Parameter ple 29 ple 30 ple 31 ple 32Δ_(1MAX) (%) 0.75 0.93 0.91 0.93 R1 (microns) 23.7 24.4 29.9 30.0 α 1.972.01 2.03 2.072 R2 (microns) 24.29 25.22 31.14 − Δ2 (%) 0 0 0 0 W2(microns) 0.58 0.83 1.27 0.00 R3 (microns) 31.08 32.93 37.92 − Δ_(3MIN)(%) −0.38 −0.33 −0.37 0 W3 (microns) 6.79 7.71 6.78 0.00 V3 (% microns²)113.3 123.5 140.5 0 R4 (microns) 62.5 62.5 62.5 62.5 Δ4 (%) 0 0 0 0Overfilled 4.16 16.99 8.01 2.47 bandwidth at 1300 nm (GHz-km) 2 × 10 mm1.49 0.95 0.73 2.53 bend loss at 1310 nm (dB) 2 × 15 mm 0.86 0.38 0.251.01 bend loss at 1310 nm (dB) 2 × 20 mm 0.53 0.17 0.12 0.53 bend lossat 1310 nm (dB) Core Diameter 45-55 45-55 62.76 60-65 (microns)Numerical Aperture 0.185-0.215 0.185-0.215 0.198 0.185-0.215 Attenuationat 0.508 0.471 0.491 1.615 1310 nm (dB/km)

Tables 6-9 summarize various modeled characteristics for the embodimentsof fiber 100 in multimode fibers examples 33-53 generally in accordancewith the invention disclosed herein and shown in FIG. 1. Various opticalproperties of the multi-mode fibers were modeled from the refractiveindex profile parameters. These parameters include the relativerefractive index Δ_(1MAX) of the core, outer core radius R₁, and thegraded index alpha (α) parameter. Additionally, the parameters includethe relative refractive index Δ₂ of the inner annular portion 40, theradius R₂ of the inner annular portion 40, and the width W₂ of the innerannular portion 40. Further, the parameters include the minimum relativerefractive index Δ_(3MIN) of the depressed-index annular portion 50, andthe outer radius R₃ of the depressed-index annular portion 50. Furthercalculations include the overfilled bandwidth at 1510 nm, 1520 nm, 1530nm, 1540 nm, 1550 nm, 1560 nm, 1570 nm, 1580 nm and 1590 nm, thedispersion and dispersion slope at 1550 nm, the attenuation at 1550 nm,the core diameter in microns, and the numerical aperture. In theexamples of Tables 6-9 the fiber has a high overfilled bandwidth (BW) inthe 1550 nm window due (a) to the core having an (Δ) value between 1.95and 2.04, and (b) the optimized width W₂ of the inner annular portion40. The optimum width for each embodiment depends on the maximumrelative refractive indices of the core, the inner annular portion andthe depressed index annular portion. These refractive index profilesenable an overfilled bandwidth greater than 2500 MHz-km at 1550 nm, andin some preferred embodiments, the overfilled bandwidth at 1310 nm isgreater than 3750, 5000 or even 7500 MHz-km. In some embodiments, theoverfilled bandwidth is greater than 2500 MHz-km at all wavelengths inthe range from 1530 to 1580 nm, and in preferred embodiments, is greaterthan 3750, 5000 or even 7500 MHz-km at all wavelengths in the range from1530 to 1580 nm. In other embodiments, the overfilled bandwidth isgreater than 2500 MHz-km at all wavelengths in the range from 1520 to1590 nm, and in preferred embodiments, is greater than 3750, 5000 oreven 7500 MHz-km at all wavelengths in the range from 1520 to 1590 nm.In other embodiments, the overfilled bandwidth is greater than 2500MHz-km at all wavelengths in the range from 1510 to 1590 nm, and inpreferred embodiments, is greater than 3750, 5000 or even 7500 MHz-km atall wavelengths in the range from 1510 to 1590 nm. In some embodiments,the overfilled bandwidth is greater than 2500 MHz-km at all wavelengthsin the range from 1500 to 1600 nm, and in preferred embodiments, isgreater than 3750, 5000 or even 7500 MHz-km at all wavelengths in therange from 1500 to 1600 nm. Preferably, the overfilled bandwidth isgreater than 2500 MHz-km at all wavelengths in the range from 1500 nm to1700 nm.

TABLE 6 Exam- Exam- Exam- Exam- Exam- ple 33 ple 34 ple 35 ple 36 ple 37Δ1 (%) 0.984 0.984 0.984 0.984 0.984 R1 (μm) 24.8 24.8 24.5 24 24 α1.979 1.980 1.981 1.982 1.982 R2 (μm) 25.62 25.45 25.6 25.15 25.22 Δ2(%) 0 0 0 0 0 W2 (μm) 0.82 0.65 1.10 1.15 1.22 R3 (μm) 31 33 31 30 30 Δ3(%) −0.32 −0.26 −0.45 −0.54 −0.63 W3 (μm) 5.38 7.55 5.40 4.85 4.78 V3(%-sq. μm) −87 −107 −121 −124 −142 R4 (μm) 62.5 62.5 62.5 62.5 62.5 Δ4(%) 0 0 0 0 0 BW1510 (Ghz-km) 10.3 12.5 10.9 11.4 8.5 BW1520 (Ghz-km)12.3 14.7 13.2 10.1 7.0 BW1530 (Ghz-km) 14.6 16.9 15.4 8.2 5.7 BW1540(Ghz-km) 16.7 17.9 15.8 20.5 20.7 BW1550 (Ghz-km) 17.7 17.7 15.8 20.320.5 BW1560 (Ghz-km) 16.0 14.8 11.0 17.1 15.0 BW1570 (Ghz-km) 13.6 12.68.7 13.8 11.9 BW1580 (Ghz-km) 11.3 10.6 14.5 11.1 9.5 BW1590 (Ghz-km)9.4 9.1 12.1 9.1 7.8 Dispersion at 19.8 19.8 19.8 19.8 19.8 1550 nm(ps/nm/km) Dispersion Slope at 0.07 0.07 0.07 0.07 0.07 1550 nm(ps/nm2/km) Attenuation at 1550 0.18 0.18 0.18 0.18 0.18 nm (dB/km) CoreDiameter (μm) 49.6 49.6 49 48 48 Numerical Aperture 0.205 0.205 0.2050.205 0.205

TABLE 7 Example 38 Example 39 Example 40 Example 41 Example 42 Example43 Δ1 (%) 0.74 0.84 0.93 1.10 1.27 1.45 R1 (μm) 24.8 24.8 24.8 24.8 24.824.8 α 1.981 1.981 1.980 1.978 1.978 1.978 R2 (μm) 25.82 25.75 25.6625.52 25.44 25.36 Δ2 (%) 0 0 0 0 0 0 W2 (μm) 1.02 0.95 0.86 0.72 0.640.56 R3 (μm) 31 31 31 31 31 31 Δ3 (%) −0.32 −0.32 −0.32 −0.32 −0.32−0.32 W3 (μm) 5.18 5.25 5.34 5.48 5.56 5.64 V3 (%-sq. μm) −83 −84 −86−89 −91 −93 R4 (μm) 62.5 62.5 62.5 62.5 62.5 62.5 Δ4 (%) 0 0 0 0 0 0BW1510 (Ghz-km) 11.3 13.1 13.8 9.9 7.3 7.7 BW1520 (Ghz-km) 10.5 15.915.2 11.3 10.1 7.5 BW1530 (Ghz-km) 21.6 19.6 15.2 12.4 10.7 7.1 BW1540(Ghz-km) 25.7 23.4 13.7 14.6 10.6 6.6 BW1550 (Ghz-km) 27.3 24.7 23.715.5 10.0 6.0 BW1560 (Ghz-km) 24.4 21.8 21.9 14.9 9.0 5.4 BW1570(Ghz-km) 19.8 17.6 18.3 13.2 8.0 4.8 BW1580 (Ghz-km) 15.8 14.0 14.8 11.37.0 4.4 BW1590 (Ghz-km) 12.8 11.4 12.1 9.5 6.2 4.0 Dispersion at 1550 nm20.4 20.2 19.9 19.5 19.1 18.7 (ps/nm/km) Dispersion Slope at 0.07 0.070.07 0.07 0.07 0.07 1550 nm (ps/nm2/km) Attenuation at 1550 0.18 0.180.18 0.18 0.18 0.18 nm (dB/km) Core Diameter (μm) 49.6 49.6 49.6 49.649.6 49.6 Numerical Aperture 0.177 0.189 0.199 0.217 0.233 0.250

TABLE 8 Example 44 Example 45 Example 46 Example 47 Example 48 Example49 Δ1 (%) 1.52 1.45 1.27 1.13 0.98 0.89 R1 (μm) 38 32.5 32.5 32.5 32 32α 1.977 1.975 1.978 1.977 1.978 1.980 R2 (μm) 39.07 33.47 33.75 33.4333.07 33.11 Δ2 (%) 0 0 0 0 0 0 W2 (μm) 1.07 0.97 1.25 0.93 1.07 1.11 R3(μm) 43 39 40 37 40 38 Δ3 (%) −0.45 −0.45 −0.5 −0.35 −0.3 −0.3 W3 (μm)3.93 5.53 6.25 3.57 6.93 4.89 V3 (%-sq. μm) −120 −160 −206 −72 −139 −90R4 (μm) 62.5 62.5 62.5 62.5 62.5 62.5 Δ4 (%) 0 0 0 0 0 0 BW1510 (Ghz-km)6.2 6.7 6.7 9.4 8.1 10.9 BW1520 (Ghz-km) 5.8 7.3 7.4 10.8 9.3 12.9BW1530 (Ghz-km) 6.2 7.5 7.9 12.1 10.9 15.5 BW1540 (Ghz-km) 5.6 7.1 8.312.7 12.8 18.7 BW1550 (Ghz-km) 5.0 6.4 8.4 12.2 14.8 21.1 BW1560(Ghz-km) 4.5 5.5 7.9 11.1 15.9 20.9 BW1570 (Ghz-km) 4.0 4.7 7.1 9.7 15.218.0 BW1580 (Ghz-km) 3.6 4.0 6.2 8.4 18.2 14.7 BW1590 (Ghz-km) 3.2 5.56.9 7.4 16.1 11.9 Dispersion at 1550 nm 18.4 18.6 19.1 19.4 19.8 20.00(ps/nm/km) Dispersion Slope at 0.07 0.07 0.07 0.07 0.07 0.07 1550 nm(ps/nm2/km) Attenuation at 1550 0.18 0.18 0.18 0.18 0.18 0.18 nm (dB/km)Core Diameter (μm) 76 65 65 65 64 64 Numerical Aperture 0.256 0.2500.233 0.220 0.204 0.194

TABLE 9 Exam- Exam- Exam- Exam- ple 50 ple 51 ple 52 ple 53 Δ1 (%) 0.990.89 0.74 0.64 R1 (μm) 21 21 21 21 α 1.980 1.980 1.982 1.982 R2 (μm)21.84 21.95 22.09 22.16 Δ2 (%) 0 0 0 0 W2 (μm) 0.84 0.95 1.09 1.16 R3(μm) 27 27 27 27 Δ3 (%) −0.4 −0.4 −0.4 −0.4 W3 (μm) 5.16 5.05 4.91 4.84V3 (%-sq. μm) −90 −87 −84 −82 R4 (μm) 62.5 62.5 62.5 62.5 Δ4 (%) 0 0 0 0BW1510 (Ghz-km) 9.5 8.8 13.0 12.7 BW1520 (Ghz-km) 11.2 10.4 15.6 11.7BW1530 (Ghz-km) 13.4 12.5 19.4 10.4 BW1540 (Ghz-km) 16.4 15.4 24.8 9.0BW1550 (Ghz-km) 19.5 19.0 31.1 37.7 BW1560 (Ghz-km) 20.9 21.7 32.6 46.1BW1570 (Ghz-km) 19.0 20.7 26.9 42.0 BW1580 (Ghz-km) 15.6 16.9 20.4 31.3BW1590 (Ghz-km) 12.6 13.3 15.7 23.1 Dispersion at 19.8 20.1 20.4 20.61550 nm (ps/nm/km) Dispersion Slope at 0.07 0.07 0.07 0.07 1550 nm(ps/nm2/km) Attenuation at 1550 0.18 0.18 0.18 0.18 nm (dB/km) CoreDiameter (μm) 42 42 42 42 Numerical Aperture 0.205 0.194 0.177 0.164

FIG. 3 illustrates a refractive index profile with the inner annularportion 30 of a fiber having an index profile as described above withrespect to FIG. 1. The example illustrated in FIG. 3 is a multimodefiber configured according to Example 1 provided in Table 1 andcomprises a graded index core and a cladding surrounding the core,wherein the cladding comprises an inner annular portion, a depressedannular portion surrounding the inner annular portion, and an outerannular portion surrounding the depressed annular portion. The core hasan outer radius R₁ of 24.8 microns and the inner annular portioncomprises a width of 0.86 microns. The glass core and the inner claddinghave alpha values that are different. FIG. 3A illustrates a refractiveindex profile and a derivative of the normalized refractive indexprofile.

FIG. 4 illustrates the measured bend loss for examples 30-32 for twoturns around a mandrel having a diameter of 15 mm. Examples 30 (squares)and 31 (triangles) comprise an inner annular segment with a depressedindex and have 2×15 mm bend losses less than 0.5 dB at 1310 nm. The 2×15mm bend loss also less than 0.5 dB at all wavelengths between 1260 and1400 nm. Example 32 (solid line) does not comprise an inner annularsegment with a depressed index and has a 2×15 mm bend loss greater thanabout 0.7 dB at 1310 nm and at all wavelengths between 1260 and 1400 nm.

FIG. 5 illustrates one embodiment of the optical transmission systemthat utilizes multimode fiber 100. According to some embodiments themulti-mode optical fiber 100 is coupled to at least one light source 204operating between 1200 nm and 1700 nm (e.g., 1260 nm to 1400 nm or 1490to 1610 nm) and modulated at a bit rate greater than 20 GHz (e.g., 25GHz). Fiber 100 is a multimode optical fiber optically and comprises agraded index a graded index glass core of 41 to 80 nm in diameter, and acladding comprising an outer cladding portion, wherein the fiber has anoverfilled bandwidth greater than 2.5 GHz-km at a wavelength of 1310 nmor 1550 nm; an alpha less than about 2.04 (and preferably less than2.03); a dispersion magnitude less than 5 ps/nm/km; and an attenuationless than 0.7 dB/km at the operating wavelength (e.g., 1310 nm, or 1550nm). A receiver or photo-detector 210 is optically coupled to themultimode optical fiber 100 and is structured to be capable of detectinga wavelength in a wavelength greater than 1200 nm, for example between1200 nm and 1700 nm (e.g., 1260 nm to 1400 nm, or 1490 to 1610 nm.

According to some embodiments the optical fiber 100 is coupled to aVCSEL, and the VCSEL is modulated at a rate greater than 20 GHz.According to some embodiments the optical fiber 100 is coupled to asilicon-photonics optical source operating in the 1200 nm to 1400 nmrange or in the 1260 to 1400 nm range (e.g., 1260 to 1360 nm, 1260 nm,1290 nm, 1310 nm, 1330 nm, 1350 nm, 1370 nm, or 1400 nm). Thus,exemplary fibers 1-28 of Tables 1 through 9 are suitable for use in anoptical transmission system. According to one embodiment, the system 200comprises: (i) a transceiver comprising at least one light source 206(e.g., VCSEL or silicon-photonics laser), wherein the light source ismodulated at a bit rate of 25 GHz or higher (and preferably, accordingto some embodiments, at 40 GHz or higher) at one or more wavelengthsbetween 1200 and 1400 nm (e.g., between 1260 and 1400 nm, or between1260 and 1360 nm, or between 1270 and 1350 nm, or between 1280 and 1340nm); (ii) at least one multimode optical fiber 100; and (iii) a receivercomprising at least one photodetector 210. In one embodiment, thetransceiver comprises N light sources modulated at a bit rate of 25 GHzor higher, as shown in FIG. 5. The transceiver may also comprise atleast one external modulator 208 which modulates the at least one lightsource at a bit rate of 25 GHz or higher. The transceiver may furthercomprise a multiplexer (Mux) 212 which multiplexes the N wavelengthsfrom N light sources into a single waveguide. The receiver may furthercomprise a demultiplexer (Demux) 212 which demultiplexes the opticalsignal into N wavelengths and optically couples them to N photodetectors210. The photodetector 210 is optically coupled to the multimode opticalfiber 100 and capable of detecting a wavelength in the 1200 to 1700 nmwavelength range.

According to some embodiments he optical fiber 100 comprises a gradedindex glass core, an inner cladding region surrounding the core and anouter cladding, and has an overfilled bandwidth at an operatingwavelength situated in the 1260 and 1400 nm wavelength range greaterthan 5 GHz-km; an alpha less than about 2.04 and preferably less than2.02; a dispersion magnitude less than 10 ps/nm/km and attenuation lessthan 0.7 dB/km at the operating wavelength. According to otherembodiments he optical fiber 100 comprises a graded index glass core, aninner cladding region surrounding the core and an outer cladding, andhas an overfilled bandwidth at an operating wavelength situated in the1490 to 1610 nm wavelength range greater than 5 GHz-km; an alpha lessthan about 2.04 and preferably less than 2.02; a dispersion magnitudeless than 10 ps/nm/km and attenuation less than 0.7 dB/km at theoperating wavelength. In some embodiments, for example, the light source206 (e.g., VCSEL or silicon-photonics laser) is modulated at a bit rateof at least 30 GHz, in some embodiments at least 35 GHz or 37 GHz, insome embodiments at least 40 GHz and in some embodiments at least 45GHz. Some embodiments of fiber have an overfilled bandwidth greater than4.7 GHz-km at one or more wavelengths between 1260 and 1360 nm, and someembodiments of fiber have an overfilled bandwidth greater than 4.7GHz-km at all wavelengths between 1290 and 1330 nm; and some embodimentsof fiber have an overfilled bandwidth greater than 4.7 GHz-km at allwavelengths between 1270 and 1350 nm.

It is noted that light sources other than VCSELS may also be utilized,for example, hybrid silicon lasers (e.g. silicon-photonic lasers)operating at wavelengths between 1200 and 1700, for example between 1200nm and 1400 nm, or 1260 nm and 1400 nm (e.g., between 1260 nm and 1360nm); or between 1490 and 1700 nm, for example 1490 to 1610 nm. Hybridsilicon lasers are made, for example, by bonding an Indium Phosphidebased wafer directly to a pre-patterned silicon photonic chip. Thistechnology is described, for example, in the publication by A. W. Fanget al., “Electrically pumped hybrid AlGaInAs-silicon evanescent laser,”Optics Express vol. 14, pp. 9203-9210 (October 2006). When a voltage isapplied to the bonded chip, the light generated from the IndiumPhosphide based material couples directly into the silicon waveguide,creating a hybrid silicon laser 206. One of the main advantages of thistechnology is the ability to incorporate many lasers onto a single chip,and the outputs from these lasers can be multiplexed into a singleoutput that is then coupled to a multimode fiber 100. For example, two,four, eight or sixteen wavelengths in the 1250-1370 nm range may bemodulated at a bit rate of 25 GHz or higher, multiplexed into a singleoutput channel, and then optically coupled to the input end of multimodefiber 100. The output end of multimode fiber 100 is optically coupled toa receiver which demultiplexes the two, four, eight or sixteenwavelengths in the 1200 to 1700 nm range (e.g., 1250-1370 nm range, or1490 to 1610 nm) and optically couples them to photodetectors capable ofdetecting the optical signals.

One embodiment of such system comprises, for example: (i) at least oneVCSEL 206, the VCSEL transmitting at a bit rate of 25 GHz or higher (andpreferably, according to some embodiments) at 40 GHz or higher at one ormore wavelengths between 1260 and 1360 nm; (ii) a multimode opticalfiber 100; and (iii) at least one photodetector 210. The multimode fiber100 for example, comprises a graded index glass core 20; an innercladding portion 30 surrounding and in contact with the core, and adepressed-index annular cladding portion 40 surrounding the innercladding portion. 30, the depressed-index annular portion 40 having arelative refractive index delta less than about −0.2% and a width of atleast 1 micron, wherein the core 20 has a radius greater than 20.5microns and less than 40 microns, a maximum relative refractive indexbetween 0.6% and 1.6% (preferably between 0.8% and 1.3%), and an alphaless than about 2.04 (preferably less than 2.03). The multimode fiber100 has, at one or more wavelengths between 1260 nm and 1360 nm orbetween 1500 and 1600 nm, an overfilled bandwidth greater than 4.7GHz-km, a dispersion magnitude less than 10 ps/nm/km and an attenuationless than 0.7 dB/km.

The above described system embodiment has one or more of the followingadvantages: energy efficiency and bit rate. Electrical power consumptionis a serious problem in modern data centers, and longer systems thatutilized longer wavelength (≧1200 nm) light sources such as VCSELs(≧1200 nm, or ≧1260 nm, or other sources) in conjunction with themultimode optical fiber 100 would mitigate some of energy consumptionproblems faced by the transmission systems operating at 850 nm. Inaddition, there appear to be significant hurdles to increasing the speedof the systems above 35 GHz-km if the of operation wavelength of thetransmission system is about 850 nm. Utilizing longer wavelength lightsources (e.g., ≧1300 nm), for example VCSELs based on In—Ga—Assemiconductors, in conjunction with the multimode optical fiber 100enables a transmission system with significantly higher transmissionspeeds (for example, ≧20 GHz, or ≧25 GHz, or ≧35 GHz, or even ≧40 GHz)than what is currently available.

It will be apparent to those skilled in the art that variousmodifications and variations can be made without departing from thespirit or scope of the claims.

What is claimed is:
 1. A multimode optical fiber comprising: a gradedindex glass core having a diameter in the range of 41 microns to 80microns, a graded index having an alpha profile wherein 1.9≦α≦2.04 and amaximum relative refractive index Δ_(1MAX) in the range between 0.6% and1.8%; and a cladding surrounding and in contact with the core, saidcladding comprising an inner annular portion surrounding and in contactwith the core with relative refractive index delta Δ₂, measured at theradius R₂ where the first derivative d(Δ/Δ_(1MAX))/d(r/R₁), is equal to−2.5; and a depressed-index annular portion surrounding the innerannular portion, wherein the fiber has an overfilled bandwidth greaterthan 2500 MHz-km at at least one wavelength between 1260 nm and 1610 nm.2. The optical fiber of claim 1, wherein (i) The fiber core has anumerical aperture NA, and 0.16<NA<0.26; (ii) the cladding comprises anouter annular portion surrounding and in contact with thedepressed-index annular portion; and (iii) the fiber has an overfilledbandwidth greater than 3750 MHz-km at 1310 nm.
 3. The optical fiber ofclaim 1, wherein (i) The fiber core has a numerical aperture NA, and0.16<NA<0.26; (ii) the cladding comprises an outer annular portionsurrounding and in contact with the depressed-index annular portion; and(iii) the fiber has an overfilled bandwidth greater than 3750 MHz-km at1550 nm.
 4. The optical fiber of claim 1, wherein the depressed-indexannular portion has a minimum relative refractive index Δ_(3MIN) lessthan −0.2% and a width of at least 1 micron.
 5. The optical fiber ofclaim 3, wherein the depressed-index annular portion has a relativeminimum refractive index Δ_(3MIN) between −0.25% and −0.7%.
 6. Theoptical fiber of claim 1, wherein the core has a maximum relativerefractive index Δ_(1MAX) between 0.7% and 1.2%.
 7. The optical fiber ofclaim 1, wherein the numerical aperture of the core is the range0.17<NA<0.23.
 8. The optical fiber of claim 1, wherein the fiber has anoverfilled bandwidth greater than 2500 MHz-km for all wavelengthsbetween: (i) 1260 nm and 1360 nm; or (ii) 1520 to 1580 nm.
 9. Theoptical fiber of claim 1, wherein the fiber has an overfilled bandwidthgreater than 3750 MHz-km for all wavelengths between: (i) 1270 nm and1350 nm, or (ii) 1530 nm and 1570 nm.
 10. The optical fiber of claim 1,wherein the fiber has an overfilled bandwidth greater than 5000 MHz-kmat either 1310 nm or 1550 nm.
 11. The optical fiber of claim 1, whereinthe fiber has an overfilled bandwidth greater than 7500 MHz-km at 1310nm.
 12. The optical fiber of claim 11, wherein the fiber has anoverfilled bandwidth greater than 5000 MHz-km for all wavelengthsbetween 1270 nm and 1350 nm.
 13. The optical fiber of claim 1, whereinthe fiber has an overfilled bandwidth greater than 7500 MHz-km at 1550nm.
 14. The optical fiber of claim 13, wherein the fiber has anoverfilled bandwidth greater than 5000 MHz-km for all wavelengthsbetween 1520 nm and 1580 nm.
 15. The optical fiber of claim 1, whereinthe core has an alpha less than 2.02.
 16. A system comprising: (i) atleast one light source transmitting at a bit rate of 25 GHz or higher atone or more operating wavelengths between 1200 and 1700 nm; (ii) atleast one multimode optical fiber optically coupled to said lightsource, said fiber comprises a graded index a graded index glass core of41 to 80 um in diameter, and a cladding comprising an outer claddingportion, wherein said fiber has an overfilled bandwidth greater than 2.5GHz-km at at least one wavelength between 1200 nm and 1700 nm; an alphaless than about 2.04; and a dispersion magnitude less than 10 ps/nm/kmand an attenuation less than 0.7 dB/km at said one or more operatingwavelengths; and (iii) a detector optically coupled to said multimodeoptical fiber and capable of detecting a wavelength in between 1200 nmto 1700 nm.
 17. A system according to claim 16, wherein said core has aradius greater than 20.5 microns and less than 40 microns, a maximumrelative refractive index Δ_(1MAX) between 0.6% and 1.6%, and said fiberhas an overfilled bandwidth greater than 5.0 GHz-km at one or morewavelengths between: (i) 1200 nm and 1400 nm; or (ii) 1500 and 1600 nm.18. A system according to claim 16, wherein said cladding comprising aninner annular portion surrounding and in contact with the core withrelative refractive index delta Δ₂, measured at the radius R₂ where thefirst derivative d(Δ/Δ_(1MAX))/d(r/R₁), is equal to −2.5; and adepressed-index annular portion surrounding the inner cladding portion,said depressed-index annular portion having a relative refractive indexdelta Δ_(3MIN) less than about −0.2% and a width of at least 1 micron,and said fiber has, an overfilled bandwidth greater than 5.0 GHz-km atone or more wavelengths between either 1200 and 1400 nm, or 1500 nm and1600 nm.
 19. A system according to claim 16, wherein said at least onelight source is at least one VCSEL.
 20. A system according to claim 16,wherein said at least one light source is at least one silicon-photonicslaser.